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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #37 : How To Solve Absolute Value Equations

Solve for .

$\left | x\right |=19$

Possible Answers:

$\pm19$

Correct answer:

$\pm19$

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve

x=19 and -x=19 .

For the second equation divide both sides by to get x=-19 .

Thus, our solutions for are,

$x=\pm19$ .

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Example Question #38 : How To Solve Absolute Value Equations

Solve for .

$\left | -x\right |=10$

Possible Answers:

$\pm10$

Correct answer:

$\pm10$

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve

-(-x)=10 and -x=10

The two negatives become positive for the first equation.

x=10

For the second equation divide both sides by to get x=-10 .

Therefore, the solutions are

$x=\pm10$ .

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Example Question #39 : How To Solve Absolute Value Equations

Solve for .

$\left | x+6\right |=19$

Possible Answers:

13, -25

-13, -25

Correct answer:

13, -25

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve

x+6=19 and -(x+6)=19 .

For the first equation subtract on both sides.

x=13

For the second equation, by distributing the negative sign, we have:

-x-6=19

From here add to both sides and divide both sides by , we get x=-25 .

Therefore, the solutions are,

x=13, -25 .

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Example Question #40 : How To Solve Absolute Value Equations

Solve for .

$\left | x+4\right |=2$

Possible Answers:

$\pm2$

2, 6

-2, -6

Correct answer:

-2, -6

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve

x+4=2 and -(x+4)=2 .

For the first equation subtract on both sides to get x=-2 .

Remember since is greater than and is negative, our answer is negative. We treat as a subtraction problem.

For the second equation, by distributing the negative sign, we have: -x-4=2 .

From here add to both sides and divide both sides by to get x=-6 .

Therefore, the solutions are,

x=-2, -6 .

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Example Question #41 : How To Solve Absolute Value Equations

Solve for .

$\left | x\right |+3=9$

Possible Answers:

$\pm6$

$\pm12$

Correct answer:

$\pm6$

Explanation:

To solve this problem we first need to isolate the variable on one side with all other constants on the other side.

$\left | x\right |+3=9$

To accomplish this perform the opposite opperation therefore subtract on both sides.

$\left | x\right |=6$

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will set up two equations to solve,

x=6 and -x=6 .

For the second equation divide both sides by to get x=-6 .

Therefore the solutions are,

$x=\pm6$ .

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Example Question #42 : How To Solve Absolute Value Equations

Solve for .

$\left | x-8\right |=17$

Possible Answers:

-9, 25

$\pm9$

$\pm25$

Correct answer:

-9, 25

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve

x-8=17 and -(x-8)=17 .

For the first equation add to both sides to get x=25 .

For the second equation, by distributing the negative sign, we have: -x+8=17 .

Now subtract to both sides and divide both sides by to get x=-9 .

Therefore, the solutions are,

x=-9, 25 .

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Example Question #43 : How To Solve Absolute Value Equations

Solve for .

$\left | x-10\right |=8$

Possible Answers:

2, 18

Correct answer:

2, 18

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve

Equation 1:

x-10=8

Add to both sides. x=18

Equation 2:

-(x-10)=8

By distributing the negative sign, we have: -x+10=8 Subtract to both sides and divide both sides by , we get x=2 . Remember, since is greater than and is negative, our answer is negative and we treat as a normal subtraction problem.

Therefore, the solutions are,

x=2, 18 .

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Example Question #44 : How To Solve Absolute Value Equations

Solve for .

$5\left | x\right |=95$

Possible Answers:

$\pm19$

Correct answer:

$\pm19$

Explanation:

First we will need to isolate the variable on one side of the equation and all other constants on the other side.

$5\left | x\right |=95$

Divide both sides by .

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve.

Equation 1:

x=19

Equation 2:

-x=19

Divide on both sides to get x=-19 .

Therefore, the solutions are,

$x=\pm19$ .

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Example Question #45 : How To Solve Absolute Value Equations

Solve for .

$\left | 3x\right |=78$

Possible Answers:

$\pm78$

$\pm26$

Correct answer:

$\pm26$

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve.

Equation 1:

3x=78

Divide on both sides. x=26 .

Equation 2:

-3x=78

Divide on both sides. x=-26 .

Therefore, the solutions are,

$x=\pm26$ .

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Example Question #46 : How To Solve Absolute Value Equations

Solve for .

$\left | 4x+5\right |=37$

Possible Answers:

$\pm8$

8, -10.5

-10.5

$\pm10.5$

Correct answer:

8, -10.5

Explanation:

When dealing with absolute value, we need to consider positive and negative values.

Therefore, we will create two separate equations to solve.

Equation 1: 4x+5=37

Subtract to both sides. Then divide to both sides. x=8

Equation 2: -(4x+5)=37

By distributing the negative sign, we have: -4x-5=37

Add to both sides and divide both sides by , we get x=-10.5 .

Therefore, the solutions are,

x=-10.5, 8 .

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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #37 : How To Solve Absolute Value Equations

Example Question #38 : How To Solve Absolute Value Equations

Example Question #39 : How To Solve Absolute Value Equations

Example Question #40 : How To Solve Absolute Value Equations

Example Question #41 : How To Solve Absolute Value Equations

Example Question #42 : How To Solve Absolute Value Equations

Example Question #43 : How To Solve Absolute Value Equations

Example Question #44 : How To Solve Absolute Value Equations

Example Question #45 : How To Solve Absolute Value Equations

Example Question #46 : How To Solve Absolute Value Equations

All Algebra 1 Resources

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